The PSS and JND are defined as
\[
\begin{align*}
pss &:= F^{-1}(0.5; \alpha, \beta) \\
jnd &:= F^{-1}(0.84; \alpha, \beta) - F^{-1}(0.5; \alpha, \beta)
\end{align*}
\]
“Slope-intercept” linear parameterization
\[
\begin{equation*}
\theta = \alpha + \beta x
\Longrightarrow
\begin{split}
pss &= -\frac{\alpha}{\beta} \\
jnd &= \frac{\mathrm{logit}(0.84)}{\beta}
\end{split}
\end{equation*}
\]
“Slope-location” linear parameterization
\[
\begin{equation*}
\theta = \beta (x - \alpha)
\Longrightarrow
\begin{split}
pss &= \alpha \\
jnd &= \frac{\mathrm{logit}(0.84)}{\beta}
\end{split}
\end{equation*}
\]